Algebras associated with Blaschke products of type {\it G}
Abstract
Let $\Omega$ and $\Omega_{\fin}$ be the sets of all interpolating Blaschke products of type $G$ and of finite type $G$, respectively. Let $E$ and $E_{\fin}$ be the Douglas algebras generated by $H^\infty$ together with the complex conjugates of elements of $\Omega$ and $\Omega_{\fin}$, respectively. We show that the set of all invertible inner functions in $E$ is the set of all finite products of elements of $\Omega$ , which is also the closure of $\Omega$ among the Blaschke products. Consequently, finite convex combinations of finite products of elements of $\Omega$ are dense in the closed unit ball of the subalgebra of $H^\infty$ generated by $\Omega$. The same results hold when we replace $\Omega$ by $\Omega_{\fin}$ and $E$ by $E_{\fin}$.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 1995
 arXiv:
 arXiv:math/9512220
 Bibcode:
 1995math.....12220G
 Keywords:

 Mathematics  Operator Algebras